Abstract
It is shown that inertial terms appear naturally in the thermodynamic theory with dual internal variables and the conditions of their appearance is well understandable in terms of mechanical notions. This demonstrates the difference between the standard single internal variable theory and the dual internal variables concept.
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References
Coleman BD, Gurtin ME (1967) Thermodynamics with internal state variables. J Chem Phys 47(2):597–613
de Groot S, Mazur P (1962) Non-equilibrium thermodynamics. North-Holland, Amsterdam
Eringen AC, Suhubi ES (1964) Nonlinear theory of simple micro-elastic solids -I. Int J Eng Sci 2(2):189–203
Horstemeyer MF, Bammann DJ (2010) Historical review of internal state variable theory for inelasticity. Int J Plast 26(9):1310–1334
Houlsby G, Puzrin A (2000) A thermomechanical framework for constitutive models for rate-independent dissipative materials. Int J Plast 16(9):1017–1047
Kestin J (1993) Internal variables in the local-equilibrium approximation. J Non-Equilib Thermodyn 18(4):360–379
Lebon G, Jou D, Casas-Vázquez J (2008) Understanding non-equilibrium thermodynamics. Springer, Berlin
Lubliner J (1973) On the structure of the rate equations of materials with internal variables. Acta Mech 17(1–2):109–119
Maugin GA (1990) Internal variables and dissipative structures. J Non-Equilib Thermodyn 15(2):173–192
Maugin GA (1994) Physical and mathematical models of nonlinear waves in solids. In: Nonlinear waves in solids. Springer, Berlin, pp 109–233
Maugin GA (2006) On the thermomechanics of continuous media with diffusion and/or weak nonlocality. Arch Appl Mech 75(10–12):723–738
Maugin GA, Muschik W (1994) Thermodynamics with internal variables. Part I. General concepts. J Non-Equilib Thermodyn 19:217–249
Mindlin RD (1964) Micro-structure in linear elasticity. Arch Rational Mech Anal 16(1):51–78
Muschik W (1990) Internal variables in non-equilibrium thermodynamics. J Non-Equilib Thermodyn 15(2):127–137
Rahouadj R, Ganghoffer JF, Cunat C (2003) A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework. Mech Res Commun 30(2):109–117
Rice JR (1971) Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J Mech Phys Solids 19(6):433–455
Rubí J, Casas-Vázquez J (1980) Thermodynamical aspects of micropolar fluids. A non-linear approach. J Non-Equilib Thermodyn 5(3):155–164
Rubí J, Pérez-Madrid A (1999) Inertial effects in non-equilibrium thermodynamics. Phys A Stat Mech Appl 264(3):492–502
Sidoroff F (1988) Internal variables and phenomenological models for metals plasticity. Revue de Physique Appliquée 23(4):649–659
Ván P (2002) Weakly nonlocal irreversible thermodynamics-the Ginzburg–Landau equation. Technische Mechanik 22(2):104–110
Ván P, Berezovski A, Engelbrecht J (2008) Internal variables and dynamic degrees of freedom. J Non-Equilib Thermodyn 33(3):235–254
Acknowledgements
This chapter is derived in part from the article published in Contin. Mech. Thermodyn., (2016) 28:1027–1037. Copyright\(\copyright \) Springer-Verlag, available online: https://link.springer.com/article/10.1007/s00161-015-0453-2
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Berezovski, A., Ván, P. (2017). Internal Variables and Microinertia. In: Internal Variables in Thermoelasticity. Solid Mechanics and Its Applications, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-319-56934-5_5
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DOI: https://doi.org/10.1007/978-3-319-56934-5_5
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